Download A new class of thermal flow sensors using /spl Delta/T=0 as a control

A New Class of Thermal Flow Sensors Using AT=O as a
Control Signal
T.S.J. Lammerink, N.R. Tas, G.J.M. Krijnen and M. Elwenspoek
MESA+ Research Institute, University of Twente, P.O. Box 21 7,7500AE Enschede,
The Netherlands. e-mail: [email protected]
The advantage of constant power driving mode is its
simple electronic implementation. This mode is often
referred to as Constant Power Anemometry or CPA.
The disadvantage is that the temperature dependence of
the fluid properties and the sensor sensitivity have to be
taken into account. This can be overcome by the
constant temperature driving mode, where the power
needed to keep a heater at constant temperature is a
measure for the flow velocity [l]. The latter method is
often referred to as Constant Temperature Anemometry
or CTA.
There is a wide variety of sensor versions with different
ways of generating stimuli and ways of measuring
response. In this paper we report on controlling a true
temperature balance between the temperature sensors
within the sensor structure. We refer to this thermal
sensor concept as Temperature Balance Anemometry or
TBA.
In the next section we will descibe the TBA method and
relate it to the existing methods.
ABSTRACT
In this paper we propose a new anemometer principle.
Next to the known Constant Power Anemometry (CPA)
and the Constant Temperature Anemometry (CTA),
here the Temperature Balanced Anemometry (TBA) is
presented. A compact overview of thermal flow sensor
system concepts is given. The new concept has
important consequenses on simple flow sensor
calibration. The proposed concept is investigated using
experiments on conventional thermal flow sensors. A
micro flow sensor is presented in combination with an
example of simple electronic interfacing circuitry.
Keywords: Anemometry, thermal flow sensor.
1. INTRODUCTION
Currently flow sensors based on thermal principles are
widely used. With a thermal flow sensor the thermal
energy tfansport (heat) which is coupled to mass
transport is exploited. In one way or another heat is
generated in a structure and the resulting fluid flow
dependent temperature distribution is monitored. In that
way the sensor system structure is that of a classical
stimulus-response measurement system (see figure 1).
2 SYSTEM MODELING
2.1 Constant Power Anemometry (CPA)
- CPA single probe
A schematic diagram of the constant power anemometer
is given in figure 2. Within the physical structure a fixed
amount of heat is dissipated in a resistor in the flow and
the resulting temperature of that resistor is a measure for
that flow. With increasing flow velocity the temperature
of the sensor decreases (see figure 3a). The temperature
of the sensor with respect to the ambient can be written
as (King’s law [2])
Fluid flow
1
Physical structure
Figure 1. General structure of a thermal flow sensor. The fluid
flow modulates a process, which is monitored by a stimulusresponse measurement.
Tl=
4
+a‘
where T, is the ambient temperature, GOthe zero flow
conductance and KO the flow sensitivity. So TI is a
function of three parameters TI = Tl(PI,v,TA.
If we want to ‘measure’ the unknown flow velocity v
with a power P1 we need to measure both Tl as well as
the ambient temperature T,.(see figure 2). Therefore we
need two temperature sensors. From the signal
difference U1-U2and the known input power PIwe can
derive the sensor systems output signal v* (the
‘measured’ flow velocity) using the flow sensor model
MCP. Ml(T1) and M2(Ta) are the (large signal)
temperature sensor transfer functions. An example
sensor model MCPis given in figure 3a.
The stimulus is a form of heat generation and an energy
transport, resulting in a response signal AT. The
temperature measurement with a temperature sensor is
absolute. This means that to measure a response signal
AT, we need two temperature sensor signals. Here lies a
source for many systematic errors in thermal flow
sensor systems. Thermal flow sensors can be divided in
different classes, based on [ 11:
1. The driving mode, constant power or constant
temperature
2. Single probe, directional insensitive, or multiprobe, directional sensitive.
0-7803-5273-4/00/$10.0082000 IEEE
+
Go KO .
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It follows that although T, is no longer used as a
reference its influence on v* is not eliminated if ml(T1)
z mz(T2) with Tl#T2.
U
Model
Physical structure
m&Q-ul
Figure 2. System structure of ‘Constant Power Anemometry’
(CPA) thermal flow sensor with single probe.
M20
In a small signal analysis we can derive for dv*
dv* = mcpd(Ul - U 2 )
Physical structure
(2)
(3)
2.2 Constant Temperature Anemometry (CTA)
- CTA single probe
With constant temperature anemometry the absolute
temperature of the temperature sensor in the physical
structure (TI, see figure 5) is kept at a constant value
above ambient (T,). Therefore this type of flow sensor
always needs a control loop [7]. The process in the
physical structure described by eqn. (1) can be rewritten
into
The physical structure is designed to have an interaction
between TI and v, but according eqn. (1) and dPI=O we
have to write dTl = slvdv+ dT, . Doing this we find
dv*=mcpml[ s l v d v + [ l - ~ ) d T a ]
(4)
Here we see that dv* also is a function of dT, unless the
sensorsensitivities ml=ml(Tl) and m2=m2(T,) are equal
for all temperatures involved. Because TI > T, it is not
possible to obtain ml(Tl) = mz(T,) if the temperature
sensor transfer functions are non-linear.
1
0
(7)
with PI=PI(v,Tl-T,). Therefore the flow velocity v can
in principle be calculated from the power required to
keep the temperature TI at a constant value above
ambient. A typical sensor model Mm is given in figure
6a. One advantage of this concept is the increase of the
effective bandwidth of the sensor system. [7]. For a
small signal analysis we first look at the open loop
structure of the CTA system (see cut in figure 5). We
than can calculate dP1* according
1
llowveloc~v
Model
Figure 4. System structure of ‘Constant Power Ane-mometry’
(CPA) differential temperature measurement thermal flow
sensor.
or with the sensor sensitivities ml(Tl)=dU1ldTl and
m2( T,)=d UddT,
dv* = mcp(mld7i - m2dT,)
-p
0 nwvdocm, v
a)
b)
Figure 3. a) CPA single probe; temperature elevation of the
temperature sensor as a function of the flow velocity. b) CPA
multi-probe; typical temperature difference between two
temperature sensors as a function of the flow velocity (see
figure 4).
or with the known sensor sensitivities ml=dUlldTl and
m2=d Uz/dT,:
- CPA multi-probe
Now the input power P1 is not longer kept constant (see
eqn.(7)), so we have to write dT, = slldP, + slvdv+ dTa ,
and we find
dP,* = p d(U1 - U , )
dP,* = p mldT, - p m2dT,
A way to omit a direct measurement of the ambient
temperature is to implement a differential temperature
measurement[3-61 (see figure 4). Furtheron, the sensor
is made directional sensitive now. A typical sensor
behavior given in figure 3b. For dv* we find
dv* = m ~ ~ d ( U- U2 , )
dP,*= P.(ml(slldP, +slvdv+dT,)-m2dT,)
(8)
(9)
(10)
in the case the loop is closed, we have dP1*=dP1so eqn.
(IO) turns into
(5)
With dTl = slvdv+ dT, and dT, = sZVdv
+ dTa we find
If the ‘open loop gain’ p mlsl1>> 1, eqn. (1 1) reduces to
(m2sZv- mlslv)dv + m2
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[:::I
dv*=mDpm2 - -scvdv-
( I+]+
1--
The flow velocity v* is calculated from the dPl* signal
and UToKset.
so we find
mDpml[ -lsCvdv
s,1+ sc2
lv
I
To eliminate the influence of an ambient temperature
change dT,, we have the next constraints for the
temperature sensor sensitivities
ITa
Physical structure
+( 1 -?)Tal
1"P
UToffset
Model
Figure 5. System structure of a 'Constant Temperature
Anemometry' (CTA) thermal flow sensor. UToff%tis used to
create a difference A(Tl-Ta).
Again we see that dv* also is a function of dTa unless
the sensor sensitivities ml(Tl) and mz(T,) are equal.
This results in a constraint for the temperature sensor
sensitivities
ml(q) = m 2 ( T a ) ,while T, > T,
Figure 7. System structure of 'Constant Temperature
Anemometry' (CTA) differential temperature measurement
(differential power) thermal flow sensor [8].The model MDP
function is comparable to the MDT function given in figure 3c
and generates the flow velocity v* as a function of the signals
and UToffset(used to create a difference A(T,-T,)).
M I ( T ~M2(T2),
),
M3(Td and Mc(Tc)are large signal temperature
sensor transfer functions.
(14)
If the flow sensor system is designed that way we now
find for the output
The system output v* does not depend on the sensor
sensitivity ml anymore.
Rowvelocny v
2.3 Temperature Balance Anemometry (TBA)
- TBA multiprobe
In this concept, the temperature difieerence between an
up-stream and a down-stream temperature sensor is kept
constant at zero, by controlled distribution of a constant
total heating power between an up-stream and a downstream heater. The ratio between the up-stream and
down-stream heating power is a measure for the fluid
flow. The absolute temperature will not be constant: at
constant total power, the average temperature of the upand downstream sensors will decrease with increasing
flow velocity. Nevertheless, this concept allows nonlinear temperature sensor transfer function as long as it
is symmetrical for the up-and downstream sensors.
Basically, as it is truly a balance measurement, the
temperature sensor pair should only indicate if the
temperature difference is smaller, equal or larger than
zero. Figure 8a shows the measurement system
structure. The flow sensor consists of two heater-sensor
pairs located in or around the flow tube, one up-stream
and one down-stream. We now assume that the heatersensor pair are located at the same position along the
0 fbw vebclv v
b)
C)
Figure 6. a) CTA single probe; heating power as a function of
the flow velocity. b) CTA multiprobe; the differential heating
power as a function of the flow velocity [8] (see figure 7).
- CTA multiprobe
The CTA concept can also be exploited in combination
with a differential temperature measurement or
differential power measurement [8] (see figure 7). An
example sensor model MDPis given in figure 6b. The
temperature T, of a reference probe in the flow sensor is
kept constant. Without going into details we state that
the system transfer function is given by
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If the ‘open loop gain’ ~ ~ ~ ( s l z - s l ~ + ~ ( s 2 1 - s 2 ~ ) > > 1 ,
and again the next constraint for the temperature sensor
sensitivities is fulfilled
ml (T,) = m2(T2), while Tl = TZ
(22)
eqn. (21) reduces to the next equation for dv*
dv *
dv
-=
pt
t
- s2v 1
- SI2 + s22 - s21
3. THERMAL MODEL
A typical example of a physical structure used in
conventional mass flow sensors is a capillary tube with
two or more heater-sensor elements. A schematic view
of such a structure is given in figure 9 (see also figure
14).
length of the tube. In general this is not necessary. The
two heaters are driven by power P1 and P2 respectively.
Their temperatures Tl resp. T2, are determined by the
heat transport in the flow sensor, which is modulated by
the flow velocity. The temperatures Tl and T2 are
measured and their difference is taken as the signal
containing the information about the flow velocity. For
a small signal analysis we look at the open loop
structure (see cut in figure 8a). We now calculate dAP*
(18)
Figure 9. Stainless steel tube with two resistors which act as a
heater as well as a temperature sensor. Two thermally highly
conductive blocks define the temperature at the tube ends at
ambient level.
or with the known sensor sensitivities ml=dUlldTl and
mz=dU,ldT2
dAP* = $ mldT, - $ m2dT2
s11
The system output v* does not depend on the sensor
sensitivities ml(T1=T2) = m2(T2=T1), anymore. The
constraint that there should be equal temperature sensor
sensitivities (eqn. (22)) now is less severe than earlier
one (eqn.(14)), because the absolute temperatures are
equal now; Tl = Tz, so the temperature sensors may be
non-linear and still fulfill the demands to eliminate the
dT, sensitivity and to cancel the temperature sensor
sensitivity from the transfer function. This is the
significant advantage for the proposed TBA concept.
Model
b)
c)
Figure 8. a) System structure of ‘Temperature Balance
Anemometry’ (TBA) thermal flow sensor. b) The relative
power difference (at T1=T2)as a function of the flow velocity.
c) The model (Mm) with the calculated flow velocity v* as a
function from the measured power signal AP* and P,.
W*= $ d(Ul - U 2 )
2blV
*B
(19)
The two resistor elements R1 and R2 are simultaneously
used as actuator as well as temperature sensor. At both
ends the tube is fixed in thermal highly conductive
blocks which are at ambient temperature. In a simplified
thermal model the tube is considered to be onedimensional with a uniform temperature in the radial
direction. We assume a effective conductivity in the x
direction equal to A,K, + Afif with A,,Af the surface
areas of the wall and the fluid and ~,,qthe thermal
conductivities of the wall and the fluid. The heat loss to
the environment at T, is modeled with a heat-transfer
coefficient h. This results in the next differential
equation for the temperature T,-T, = T,
rewriting the temperature variations dTl and dT2 and
writing dP1 and dP2 in terms of dAP* (closed loop and
assuming dPpO) results in
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in a resistor is measured by measuring the current
through and the voltage over the resistor using a four
point measurement method. In this way the dissipated
power is known independent from the actual resistor
value (PR(T)~R(T)*VR(T)).At the same time the
temperature from the resistor is calculated from the
measured actual resistor value (R(T)=VR(T)/ZR(T)) and a
known calibration formula for that resistor
with p the fluid density, c the fluid heat capacity at
constant pressure and v the flow velocity. Equation (24)
is a second order linear differential equation in T,,.
Solving the differential equation results in the general
temperature distribution function
T, ( x ) = a exp(Ax>+ P exp(+)
(254
with
=
R(T) = RT,(l
vk,/v2 +4h(A,Kw +AfKf)/A?p2c2
2[A,Kw
+ Af Kf )/Af
(25b)
+ a(T - T,))
(26)
The results obtained with these experiments are given in
figure 15 and are in good qualitative agreement with the
theory.
pC
and a and P depending on the boundary conditions. In
order to solve the temperature distribution, the sensor
structure is devised into three parts, each with its own
boundary conditions. In the configuration of figure 9
with the TBA method, the boundary conditions are
T,(O)=T,(L)=O and T,(xl) = Tm(x2). The temperature
amplitude is found from the heat balance and P1+P2=P1.
The temperature distribution for three different flow
velocities is given in figure l l a . The relative power
difference (P1-P2)/Ptis given in figure 1lb.
Air
Figure 13. Measurement setup forpautomatic controlling the
heater powers and for measuring the resistor temperatures.
0
0.2
0.6
0.4
0.8
X
Figure 14. Photograph of the capillary tube flow sensing
structure used in our experiments. The tube inner and outer
diameter are 0.4 mm and 0.7 mm respectively. Six wire wound
resistors (length 3 mm) can act as heater-sensor elements.
-,-
-3
-a0
-IO
IO
0
a0
I)
Info out:
V
Figure 11. a) Temperature distribution of''7 as a function of
the relative position n on the tube for three different flows.
b) The calculated relative power difference (Pl-Pz)lPtof the
two heaters RIand Rzas a function of the flow velocity.
s+f:
......................
-
.J
I
4. EXPERIMENTS
-m
.........................
0
-0.3
-05
I
I
1
m
0
___t
Flow [sccm]
First experiments on the concept are carried out on a
conventional flow sensor tube consisting of a stainless
steel hollow tube (0.4 x 0.7 mm 9) with 6 wire wound
resistors around it (each 3 mm long) which can act as a
sensor as well as an actuator (see figure 14). A
schematic view of the measurement setup with the
sensor tube is given in figure 13. The fluid flow through
the tube is steered by a mass flow controller. The
system controller in the setup is implemented on a
personal computer using Labview. The power dissipated
Figure 15. Output signal of the controller (P~-P&P~+Pz)as a
function of the applied flow. The square blocks are the
measured points. The continuous line is the model result as
shown in figure 12 and fitted with a scale factor for (Pl-Pz)/P,.
In a second experiment the TBA system is implemented
using a micro flow sensor as physical structure (see
figure 16a and figure 17b). The electronic TBA
controller was designed around a thermal oscillator (see
figure 16b and figure 17a). The sensor system is tested
529
with a flow velocity v from -2 d s to 2 d s . The pulse
width modulated ouput signal of the oscillator is linear
with the flow velocity and varies in the experiment from
45% to 55%.
methods the sensitivity of the sensor output for changes
of the ambient temperature can be eliminated if in the
whole measurement range the temperature sensor
sensitivities are equal. In all but the TBA method this
implies that temperature dependent sensitivities are not
allowed, which means that the transfer functions of the
temperature sensors should be linear. In the TBA
method temperature symmetry is maintained, which
means that the temperature sensors with equal
temperature dependent transfer functions are allowed,
also non-linear ones. This opens the way towards the
use of for example highly sensitive metalsemiconductor thermocouples, which are strongly nonlinear but provide good symmetry. Two experiments
have shown the feasability of the TBA method.
a)
b)
Figure 16. a) Photograph of the micro flow sensor structure
with four meander shaped thin film resistors. For a cross
section see figure 17b. b) Photograph of a TBA sensor system
with the micro sensor on the tip of a stick and the TBA
controller mounted on a 1” x 1” PC-board.
6. ACKNOWLEDGEMENTS
The authors wish to thank J.W. Berenschot for realizing
the silicon test samples.
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U
E
4
L
I
Imo
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tl+tZ
Figure 17. a) Schematic diagram of a relative simple thermal
oscillator [see also 101 used as a TBA controller. The timing
of the output signal ((tl-rz)/(rl+tz))directly represents the
AP/P, signal. b) Cross section of the micro flow sensor. The
resistors are supported by 1 pm thick and 80 pm wide silicon
nitride bridges at 40 pm distance from each other.
5. DISCUSSION & CONCLUSIONS
We have introduced a new flow measurement method
based on a dual probe thermal flow sensor: Temperature
Balance Anemometry (TBA). Four existing thermal
flow sensor measurement methods have been analyzed
and compared with the TBA: CPA single and dual
probe, CTA single and multi-probe. In both the CTA
single probe, and the TBA dual probe method, the flow
measurement is based on thermal balance, and if
temperature sensors symmetry is provided the
temperature sensor transfer function is eliminated in the
flow sensor transfer function. In the TBA method the
sensor output is derived from the distribution of the
heating powers between the two heatedsensor couples.
This means that the sensor transfer function is
completely determined by the thermal and the flow
properties of the sensor. In all five of the analyzed
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